2.4. Random Survival Forests

Concept

Random survival forests, an ensemble method for analysing right censored data, first introduced by Ishwaran et al, 2008. RSF has several advantages over Cox regression: (i) Unlike Cox regression, RSF does not rely on proportional hazard assumption. (ii) RSF accounts for nonlinear effects and interactions for factor variables.

Usage

A random survival forests analysis can be conducted by applying the following steps:

1. Select the analysis method as Random Survival Forests from Analysis tab.
2. Select suitable variables for the analysis, such as survival time, status variable, category value for status variable, and categorical and continuous predictors for the model.
3. In advanced options, interaction terms, strata terms and time dependent covariates can be added to the model. Moreover, if there are multiple records for observations, users can specify it by clicking Multiple ID checkbox. From RSF options, number of tree, bootstrap method, randomly selected number of variable, minimum number of cases in terminal node, maximum depth for a tree, splitting rule, number of split, missing values, number of iterations of the missing data algorithm, proximity of cases, size of bootstrap and type of bootstrap can be adjusted.
4. Click Run button to run the analysis.

Outputs

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## Trees Grown:     710,    Time Remaining (sec):       1

a. Individual Survival Predictions

Survival predictions for each observation can be obtained. In this table, rows represent observations whereas columns represent time endpoints.

b. Individual Survival Predictions OOB

Out of bag (OOB) survival predictions for each observation can be obtained. In this table, rows represent observations whereas columns represent time endpoints.

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c. Individual Cumulative Hazard Predictions

Cumulative hazard predictions for each observation can be obtained. In this table, rows represent observations whereas columns represent time endpoints.

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d. Individual Cumulative Hazard Predictions OOB

Out of bag (OOB) cumulative hazard predictions for each observation can be obtained. In this table, rows represent observations whereas columns represent time endpoints.

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e. Error Rate

An error rate table, which shows error rate estimations for each tree, can be obtained.

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f. Variable Importance

A variable importance table as well as an interactive plot, which shows relative importance of variables in fitted model, can be obtained.

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g. Overall Survival Plot

A survival plot can be created based on Nelson-Aalen estimator and overall ensemble predictions.

h. Individual Random Survival Plot

A survival plot can be drawn for survival predictions from random survival forests model. Each line represents a survival curve for each observation.

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i. Individual Survival OOB Plot

A survival plot can be drawn for OOB survival predictions from random survival forests model. Each line represents a survival curve for each observation.

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j. Individual Cumulative Hazard Plot

A cumulative hazard plot can be drawn for hazard predictions from random survival forests model. Each line represents a survival curve for each observation.

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k. Individual Cumulative Hazard OOB Plot

A cumulative hazard plot can be drawn for OOB cumulative hazard predictions from random survival forests model. Each line represents a survival curve for each observation.

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l. Error Rate Plot

An interactive error rate plot, which shows error rate alterations when number of trees increased, can be drawn.

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m. Cox vs RSF

A Cox model can be compared to random survival forests model through an interactive plot for visual inspection of both models.

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## Trees Grown:     664,    Time Remaining (sec):       2